Bing's Theorem

If $M^3$ is a closed oriented connected 3-Manifold such that every simple closed curve in $M$ lies interior to a Ball in $M$, then $M$ is Homeomorphic with the Hypersphere, $\Bbb{S}^3$.

See also Ball, Hypersphere

References

Bing, R. H. ``Necessary and Sufficient Conditions that a 3-Manifold be $S^3$.'' Ann. Math. 68, 17-37, 1958.

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 251-257, 1976.